Properties

Label 6029.2.a.a.1.18
Level $6029$
Weight $2$
Character 6029.1
Self dual yes
Analytic conductor $48.142$
Analytic rank $1$
Dimension $234$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6029,2,Mod(1,6029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6029 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6029.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.1418073786\)
Analytic rank: \(1\)
Dimension: \(234\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 6029.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.45423 q^{2} +2.05779 q^{3} +4.02326 q^{4} -1.79809 q^{5} -5.05030 q^{6} +3.33599 q^{7} -4.96555 q^{8} +1.23450 q^{9} +O(q^{10})\) \(q-2.45423 q^{2} +2.05779 q^{3} +4.02326 q^{4} -1.79809 q^{5} -5.05030 q^{6} +3.33599 q^{7} -4.96555 q^{8} +1.23450 q^{9} +4.41293 q^{10} +2.39546 q^{11} +8.27902 q^{12} -6.12503 q^{13} -8.18729 q^{14} -3.70009 q^{15} +4.14010 q^{16} -4.09021 q^{17} -3.02975 q^{18} +1.64645 q^{19} -7.23418 q^{20} +6.86476 q^{21} -5.87901 q^{22} -1.16024 q^{23} -10.2181 q^{24} -1.76687 q^{25} +15.0323 q^{26} -3.63303 q^{27} +13.4215 q^{28} +8.83975 q^{29} +9.08089 q^{30} -9.45409 q^{31} -0.229666 q^{32} +4.92935 q^{33} +10.0383 q^{34} -5.99841 q^{35} +4.96671 q^{36} -0.0716628 q^{37} -4.04078 q^{38} -12.6040 q^{39} +8.92851 q^{40} +6.84880 q^{41} -16.8477 q^{42} +7.58637 q^{43} +9.63755 q^{44} -2.21974 q^{45} +2.84749 q^{46} +5.93310 q^{47} +8.51945 q^{48} +4.12882 q^{49} +4.33632 q^{50} -8.41678 q^{51} -24.6426 q^{52} +5.04954 q^{53} +8.91630 q^{54} -4.30725 q^{55} -16.5650 q^{56} +3.38805 q^{57} -21.6948 q^{58} +5.49282 q^{59} -14.8864 q^{60} +3.13441 q^{61} +23.2025 q^{62} +4.11827 q^{63} -7.71654 q^{64} +11.0134 q^{65} -12.0978 q^{66} +2.64537 q^{67} -16.4560 q^{68} -2.38752 q^{69} +14.7215 q^{70} -6.30184 q^{71} -6.12997 q^{72} -7.88700 q^{73} +0.175877 q^{74} -3.63585 q^{75} +6.62411 q^{76} +7.99122 q^{77} +30.9332 q^{78} -12.1333 q^{79} -7.44427 q^{80} -11.1795 q^{81} -16.8085 q^{82} -11.0120 q^{83} +27.6187 q^{84} +7.35456 q^{85} -18.6187 q^{86} +18.1904 q^{87} -11.8948 q^{88} -7.98323 q^{89} +5.44776 q^{90} -20.4330 q^{91} -4.66793 q^{92} -19.4545 q^{93} -14.5612 q^{94} -2.96047 q^{95} -0.472605 q^{96} -17.2257 q^{97} -10.1331 q^{98} +2.95719 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45423 −1.73540 −0.867702 0.497084i \(-0.834404\pi\)
−0.867702 + 0.497084i \(0.834404\pi\)
\(3\) 2.05779 1.18807 0.594033 0.804441i \(-0.297535\pi\)
0.594033 + 0.804441i \(0.297535\pi\)
\(4\) 4.02326 2.01163
\(5\) −1.79809 −0.804130 −0.402065 0.915611i \(-0.631707\pi\)
−0.402065 + 0.915611i \(0.631707\pi\)
\(6\) −5.05030 −2.06177
\(7\) 3.33599 1.26088 0.630442 0.776236i \(-0.282873\pi\)
0.630442 + 0.776236i \(0.282873\pi\)
\(8\) −4.96555 −1.75559
\(9\) 1.23450 0.411500
\(10\) 4.41293 1.39549
\(11\) 2.39546 0.722258 0.361129 0.932516i \(-0.382391\pi\)
0.361129 + 0.932516i \(0.382391\pi\)
\(12\) 8.27902 2.38995
\(13\) −6.12503 −1.69878 −0.849389 0.527768i \(-0.823029\pi\)
−0.849389 + 0.527768i \(0.823029\pi\)
\(14\) −8.18729 −2.18815
\(15\) −3.70009 −0.955360
\(16\) 4.14010 1.03502
\(17\) −4.09021 −0.992021 −0.496010 0.868317i \(-0.665202\pi\)
−0.496010 + 0.868317i \(0.665202\pi\)
\(18\) −3.02975 −0.714118
\(19\) 1.64645 0.377722 0.188861 0.982004i \(-0.439520\pi\)
0.188861 + 0.982004i \(0.439520\pi\)
\(20\) −7.23418 −1.61761
\(21\) 6.86476 1.49801
\(22\) −5.87901 −1.25341
\(23\) −1.16024 −0.241926 −0.120963 0.992657i \(-0.538598\pi\)
−0.120963 + 0.992657i \(0.538598\pi\)
\(24\) −10.2181 −2.08575
\(25\) −1.76687 −0.353374
\(26\) 15.0323 2.94807
\(27\) −3.63303 −0.699177
\(28\) 13.4215 2.53643
\(29\) 8.83975 1.64150 0.820750 0.571287i \(-0.193556\pi\)
0.820750 + 0.571287i \(0.193556\pi\)
\(30\) 9.08089 1.65794
\(31\) −9.45409 −1.69801 −0.849003 0.528389i \(-0.822796\pi\)
−0.849003 + 0.528389i \(0.822796\pi\)
\(32\) −0.229666 −0.0405997
\(33\) 4.92935 0.858090
\(34\) 10.0383 1.72156
\(35\) −5.99841 −1.01392
\(36\) 4.96671 0.827785
\(37\) −0.0716628 −0.0117813 −0.00589065 0.999983i \(-0.501875\pi\)
−0.00589065 + 0.999983i \(0.501875\pi\)
\(38\) −4.04078 −0.655501
\(39\) −12.6040 −2.01826
\(40\) 8.92851 1.41172
\(41\) 6.84880 1.06960 0.534801 0.844978i \(-0.320386\pi\)
0.534801 + 0.844978i \(0.320386\pi\)
\(42\) −16.8477 −2.59966
\(43\) 7.58637 1.15691 0.578455 0.815714i \(-0.303656\pi\)
0.578455 + 0.815714i \(0.303656\pi\)
\(44\) 9.63755 1.45292
\(45\) −2.21974 −0.330899
\(46\) 2.84749 0.419839
\(47\) 5.93310 0.865431 0.432716 0.901530i \(-0.357555\pi\)
0.432716 + 0.901530i \(0.357555\pi\)
\(48\) 8.51945 1.22968
\(49\) 4.12882 0.589831
\(50\) 4.33632 0.613248
\(51\) −8.41678 −1.17859
\(52\) −24.6426 −3.41731
\(53\) 5.04954 0.693608 0.346804 0.937938i \(-0.387267\pi\)
0.346804 + 0.937938i \(0.387267\pi\)
\(54\) 8.91630 1.21336
\(55\) −4.30725 −0.580790
\(56\) −16.5650 −2.21359
\(57\) 3.38805 0.448759
\(58\) −21.6948 −2.84867
\(59\) 5.49282 0.715104 0.357552 0.933893i \(-0.383612\pi\)
0.357552 + 0.933893i \(0.383612\pi\)
\(60\) −14.8864 −1.92183
\(61\) 3.13441 0.401321 0.200660 0.979661i \(-0.435691\pi\)
0.200660 + 0.979661i \(0.435691\pi\)
\(62\) 23.2025 2.94673
\(63\) 4.11827 0.518854
\(64\) −7.71654 −0.964568
\(65\) 11.0134 1.36604
\(66\) −12.0978 −1.48913
\(67\) 2.64537 0.323184 0.161592 0.986858i \(-0.448337\pi\)
0.161592 + 0.986858i \(0.448337\pi\)
\(68\) −16.4560 −1.99558
\(69\) −2.38752 −0.287424
\(70\) 14.7215 1.75955
\(71\) −6.30184 −0.747891 −0.373945 0.927451i \(-0.621995\pi\)
−0.373945 + 0.927451i \(0.621995\pi\)
\(72\) −6.12997 −0.722424
\(73\) −7.88700 −0.923103 −0.461552 0.887113i \(-0.652707\pi\)
−0.461552 + 0.887113i \(0.652707\pi\)
\(74\) 0.175877 0.0204453
\(75\) −3.63585 −0.419832
\(76\) 6.62411 0.759837
\(77\) 7.99122 0.910684
\(78\) 30.9332 3.50250
\(79\) −12.1333 −1.36510 −0.682551 0.730838i \(-0.739130\pi\)
−0.682551 + 0.730838i \(0.739130\pi\)
\(80\) −7.44427 −0.832295
\(81\) −11.1795 −1.24217
\(82\) −16.8085 −1.85619
\(83\) −11.0120 −1.20872 −0.604362 0.796709i \(-0.706572\pi\)
−0.604362 + 0.796709i \(0.706572\pi\)
\(84\) 27.6187 3.01345
\(85\) 7.35456 0.797714
\(86\) −18.6187 −2.00771
\(87\) 18.1904 1.95021
\(88\) −11.8948 −1.26799
\(89\) −7.98323 −0.846221 −0.423111 0.906078i \(-0.639062\pi\)
−0.423111 + 0.906078i \(0.639062\pi\)
\(90\) 5.44776 0.574244
\(91\) −20.4330 −2.14196
\(92\) −4.66793 −0.486665
\(93\) −19.4545 −2.01734
\(94\) −14.5612 −1.50187
\(95\) −2.96047 −0.303738
\(96\) −0.472605 −0.0482351
\(97\) −17.2257 −1.74900 −0.874501 0.485024i \(-0.838811\pi\)
−0.874501 + 0.485024i \(0.838811\pi\)
\(98\) −10.1331 −1.02360
\(99\) 2.95719 0.297209
\(100\) −7.10858 −0.710858
\(101\) 6.33659 0.630514 0.315257 0.949006i \(-0.397909\pi\)
0.315257 + 0.949006i \(0.397909\pi\)
\(102\) 20.6567 2.04532
\(103\) −4.14282 −0.408204 −0.204102 0.978950i \(-0.565427\pi\)
−0.204102 + 0.978950i \(0.565427\pi\)
\(104\) 30.4141 2.98235
\(105\) −12.3435 −1.20460
\(106\) −12.3928 −1.20369
\(107\) 7.49093 0.724175 0.362088 0.932144i \(-0.382064\pi\)
0.362088 + 0.932144i \(0.382064\pi\)
\(108\) −14.6166 −1.40649
\(109\) −4.90706 −0.470011 −0.235006 0.971994i \(-0.575511\pi\)
−0.235006 + 0.971994i \(0.575511\pi\)
\(110\) 10.5710 1.00791
\(111\) −0.147467 −0.0139969
\(112\) 13.8113 1.30505
\(113\) 14.9221 1.40375 0.701876 0.712300i \(-0.252346\pi\)
0.701876 + 0.712300i \(0.252346\pi\)
\(114\) −8.31507 −0.778778
\(115\) 2.08621 0.194540
\(116\) 35.5646 3.30209
\(117\) −7.56134 −0.699046
\(118\) −13.4806 −1.24099
\(119\) −13.6449 −1.25082
\(120\) 18.3730 1.67722
\(121\) −5.26178 −0.478343
\(122\) −7.69258 −0.696454
\(123\) 14.0934 1.27076
\(124\) −38.0363 −3.41576
\(125\) 12.1674 1.08829
\(126\) −10.1072 −0.900421
\(127\) 13.6509 1.21132 0.605659 0.795724i \(-0.292909\pi\)
0.605659 + 0.795724i \(0.292909\pi\)
\(128\) 19.3975 1.71452
\(129\) 15.6112 1.37449
\(130\) −27.0293 −2.37063
\(131\) −13.6674 −1.19412 −0.597061 0.802196i \(-0.703665\pi\)
−0.597061 + 0.802196i \(0.703665\pi\)
\(132\) 19.8321 1.72616
\(133\) 5.49255 0.476264
\(134\) −6.49237 −0.560855
\(135\) 6.53252 0.562229
\(136\) 20.3101 1.74158
\(137\) −9.99634 −0.854045 −0.427022 0.904241i \(-0.640437\pi\)
−0.427022 + 0.904241i \(0.640437\pi\)
\(138\) 5.85953 0.498797
\(139\) −18.1146 −1.53646 −0.768232 0.640171i \(-0.778863\pi\)
−0.768232 + 0.640171i \(0.778863\pi\)
\(140\) −24.1332 −2.03962
\(141\) 12.2091 1.02819
\(142\) 15.4662 1.29789
\(143\) −14.6723 −1.22696
\(144\) 5.11095 0.425912
\(145\) −15.8947 −1.31998
\(146\) 19.3565 1.60196
\(147\) 8.49624 0.700758
\(148\) −0.288318 −0.0236996
\(149\) 5.29357 0.433666 0.216833 0.976209i \(-0.430427\pi\)
0.216833 + 0.976209i \(0.430427\pi\)
\(150\) 8.92323 0.728578
\(151\) −21.0927 −1.71650 −0.858249 0.513234i \(-0.828447\pi\)
−0.858249 + 0.513234i \(0.828447\pi\)
\(152\) −8.17554 −0.663124
\(153\) −5.04935 −0.408216
\(154\) −19.6123 −1.58041
\(155\) 16.9993 1.36542
\(156\) −50.7093 −4.05999
\(157\) 5.60951 0.447688 0.223844 0.974625i \(-0.428139\pi\)
0.223844 + 0.974625i \(0.428139\pi\)
\(158\) 29.7779 2.36901
\(159\) 10.3909 0.824052
\(160\) 0.412961 0.0326474
\(161\) −3.87053 −0.305041
\(162\) 27.4371 2.15566
\(163\) 14.5856 1.14243 0.571216 0.820800i \(-0.306472\pi\)
0.571216 + 0.820800i \(0.306472\pi\)
\(164\) 27.5545 2.15164
\(165\) −8.86342 −0.690016
\(166\) 27.0260 2.09763
\(167\) −22.0799 −1.70859 −0.854295 0.519788i \(-0.826011\pi\)
−0.854295 + 0.519788i \(0.826011\pi\)
\(168\) −34.0873 −2.62989
\(169\) 24.5160 1.88585
\(170\) −18.0498 −1.38436
\(171\) 2.03254 0.155433
\(172\) 30.5219 2.32728
\(173\) −21.2826 −1.61809 −0.809043 0.587749i \(-0.800014\pi\)
−0.809043 + 0.587749i \(0.800014\pi\)
\(174\) −44.6434 −3.38440
\(175\) −5.89426 −0.445564
\(176\) 9.91744 0.747555
\(177\) 11.3031 0.849590
\(178\) 19.5927 1.46854
\(179\) −21.8814 −1.63549 −0.817746 0.575580i \(-0.804776\pi\)
−0.817746 + 0.575580i \(0.804776\pi\)
\(180\) −8.93059 −0.665647
\(181\) −1.02528 −0.0762087 −0.0381043 0.999274i \(-0.512132\pi\)
−0.0381043 + 0.999274i \(0.512132\pi\)
\(182\) 50.1474 3.71717
\(183\) 6.44996 0.476795
\(184\) 5.76121 0.424722
\(185\) 0.128856 0.00947369
\(186\) 47.7460 3.50090
\(187\) −9.79792 −0.716495
\(188\) 23.8704 1.74093
\(189\) −12.1197 −0.881582
\(190\) 7.26568 0.527108
\(191\) −19.4767 −1.40929 −0.704643 0.709562i \(-0.748893\pi\)
−0.704643 + 0.709562i \(0.748893\pi\)
\(192\) −15.8790 −1.14597
\(193\) 8.33075 0.599660 0.299830 0.953993i \(-0.403070\pi\)
0.299830 + 0.953993i \(0.403070\pi\)
\(194\) 42.2758 3.03523
\(195\) 22.6632 1.62294
\(196\) 16.6113 1.18652
\(197\) 10.7810 0.768117 0.384059 0.923309i \(-0.374526\pi\)
0.384059 + 0.923309i \(0.374526\pi\)
\(198\) −7.25764 −0.515778
\(199\) −10.0163 −0.710036 −0.355018 0.934859i \(-0.615525\pi\)
−0.355018 + 0.934859i \(0.615525\pi\)
\(200\) 8.77349 0.620380
\(201\) 5.44362 0.383964
\(202\) −15.5515 −1.09420
\(203\) 29.4893 2.06974
\(204\) −33.8629 −2.37088
\(205\) −12.3148 −0.860100
\(206\) 10.1674 0.708400
\(207\) −1.43231 −0.0995524
\(208\) −25.3582 −1.75828
\(209\) 3.94401 0.272813
\(210\) 30.2937 2.09047
\(211\) 1.72654 0.118860 0.0594300 0.998232i \(-0.481072\pi\)
0.0594300 + 0.998232i \(0.481072\pi\)
\(212\) 20.3156 1.39528
\(213\) −12.9679 −0.888543
\(214\) −18.3845 −1.25674
\(215\) −13.6410 −0.930307
\(216\) 18.0400 1.22747
\(217\) −31.5387 −2.14099
\(218\) 12.0431 0.815660
\(219\) −16.2298 −1.09671
\(220\) −17.3292 −1.16833
\(221\) 25.0526 1.68522
\(222\) 0.361918 0.0242904
\(223\) −11.2786 −0.755274 −0.377637 0.925954i \(-0.623263\pi\)
−0.377637 + 0.925954i \(0.623263\pi\)
\(224\) −0.766165 −0.0511915
\(225\) −2.18120 −0.145413
\(226\) −36.6223 −2.43608
\(227\) −17.1229 −1.13649 −0.568245 0.822859i \(-0.692377\pi\)
−0.568245 + 0.822859i \(0.692377\pi\)
\(228\) 13.6310 0.902736
\(229\) −7.02069 −0.463940 −0.231970 0.972723i \(-0.574517\pi\)
−0.231970 + 0.972723i \(0.574517\pi\)
\(230\) −5.12004 −0.337606
\(231\) 16.4443 1.08195
\(232\) −43.8942 −2.88180
\(233\) 25.2366 1.65331 0.826654 0.562711i \(-0.190242\pi\)
0.826654 + 0.562711i \(0.190242\pi\)
\(234\) 18.5573 1.21313
\(235\) −10.6682 −0.695920
\(236\) 22.0990 1.43852
\(237\) −24.9678 −1.62183
\(238\) 33.4877 2.17069
\(239\) 16.1821 1.04673 0.523366 0.852108i \(-0.324676\pi\)
0.523366 + 0.852108i \(0.324676\pi\)
\(240\) −15.3187 −0.988821
\(241\) −20.4815 −1.31933 −0.659664 0.751561i \(-0.729301\pi\)
−0.659664 + 0.751561i \(0.729301\pi\)
\(242\) 12.9136 0.830119
\(243\) −12.1060 −0.776600
\(244\) 12.6106 0.807308
\(245\) −7.42398 −0.474301
\(246\) −34.5885 −2.20528
\(247\) −10.0846 −0.641666
\(248\) 46.9448 2.98100
\(249\) −22.6604 −1.43604
\(250\) −29.8617 −1.88862
\(251\) −21.7112 −1.37040 −0.685200 0.728355i \(-0.740285\pi\)
−0.685200 + 0.728355i \(0.740285\pi\)
\(252\) 16.5689 1.04374
\(253\) −2.77930 −0.174733
\(254\) −33.5024 −2.10213
\(255\) 15.1341 0.947736
\(256\) −32.1730 −2.01081
\(257\) −30.5269 −1.90421 −0.952107 0.305764i \(-0.901088\pi\)
−0.952107 + 0.305764i \(0.901088\pi\)
\(258\) −38.3134 −2.38529
\(259\) −0.239066 −0.0148549
\(260\) 44.3096 2.74796
\(261\) 10.9127 0.675477
\(262\) 33.5429 2.07229
\(263\) 12.2414 0.754836 0.377418 0.926043i \(-0.376812\pi\)
0.377418 + 0.926043i \(0.376812\pi\)
\(264\) −24.4769 −1.50645
\(265\) −9.07953 −0.557751
\(266\) −13.4800 −0.826511
\(267\) −16.4278 −1.00537
\(268\) 10.6430 0.650126
\(269\) −5.18245 −0.315979 −0.157990 0.987441i \(-0.550501\pi\)
−0.157990 + 0.987441i \(0.550501\pi\)
\(270\) −16.0323 −0.975696
\(271\) 7.40101 0.449579 0.224790 0.974407i \(-0.427831\pi\)
0.224790 + 0.974407i \(0.427831\pi\)
\(272\) −16.9339 −1.02677
\(273\) −42.0469 −2.54479
\(274\) 24.5333 1.48211
\(275\) −4.23247 −0.255227
\(276\) −9.60562 −0.578190
\(277\) 9.22650 0.554367 0.277183 0.960817i \(-0.410599\pi\)
0.277183 + 0.960817i \(0.410599\pi\)
\(278\) 44.4576 2.66639
\(279\) −11.6711 −0.698729
\(280\) 29.7854 1.78002
\(281\) −13.2871 −0.792643 −0.396322 0.918112i \(-0.629714\pi\)
−0.396322 + 0.918112i \(0.629714\pi\)
\(282\) −29.9639 −1.78432
\(283\) 21.8447 1.29853 0.649266 0.760562i \(-0.275076\pi\)
0.649266 + 0.760562i \(0.275076\pi\)
\(284\) −25.3539 −1.50448
\(285\) −6.09203 −0.360860
\(286\) 36.0091 2.12927
\(287\) 22.8475 1.34865
\(288\) −0.283523 −0.0167068
\(289\) −0.270221 −0.0158953
\(290\) 39.0092 2.29070
\(291\) −35.4468 −2.07793
\(292\) −31.7314 −1.85694
\(293\) 12.6445 0.738700 0.369350 0.929290i \(-0.379580\pi\)
0.369350 + 0.929290i \(0.379580\pi\)
\(294\) −20.8517 −1.21610
\(295\) −9.87658 −0.575037
\(296\) 0.355845 0.0206831
\(297\) −8.70277 −0.504986
\(298\) −12.9917 −0.752587
\(299\) 7.10648 0.410978
\(300\) −14.6280 −0.844546
\(301\) 25.3080 1.45873
\(302\) 51.7663 2.97882
\(303\) 13.0394 0.749092
\(304\) 6.81648 0.390952
\(305\) −5.63596 −0.322714
\(306\) 12.3923 0.708420
\(307\) −16.1229 −0.920184 −0.460092 0.887871i \(-0.652184\pi\)
−0.460092 + 0.887871i \(0.652184\pi\)
\(308\) 32.1508 1.83196
\(309\) −8.52505 −0.484973
\(310\) −41.7203 −2.36955
\(311\) −10.0487 −0.569810 −0.284905 0.958556i \(-0.591962\pi\)
−0.284905 + 0.958556i \(0.591962\pi\)
\(312\) 62.5859 3.54323
\(313\) −27.0102 −1.52671 −0.763353 0.645982i \(-0.776448\pi\)
−0.763353 + 0.645982i \(0.776448\pi\)
\(314\) −13.7671 −0.776920
\(315\) −7.40503 −0.417226
\(316\) −48.8154 −2.74608
\(317\) −4.47449 −0.251312 −0.125656 0.992074i \(-0.540104\pi\)
−0.125656 + 0.992074i \(0.540104\pi\)
\(318\) −25.5017 −1.43006
\(319\) 21.1753 1.18559
\(320\) 13.8750 0.775638
\(321\) 15.4148 0.860368
\(322\) 9.49919 0.529369
\(323\) −6.73433 −0.374708
\(324\) −44.9781 −2.49878
\(325\) 10.8221 0.600304
\(326\) −35.7964 −1.98258
\(327\) −10.0977 −0.558404
\(328\) −34.0081 −1.87778
\(329\) 19.7927 1.09121
\(330\) 21.7529 1.19746
\(331\) 7.29370 0.400898 0.200449 0.979704i \(-0.435760\pi\)
0.200449 + 0.979704i \(0.435760\pi\)
\(332\) −44.3042 −2.43151
\(333\) −0.0884676 −0.00484800
\(334\) 54.1891 2.96510
\(335\) −4.75662 −0.259882
\(336\) 28.4208 1.55048
\(337\) 11.3404 0.617749 0.308875 0.951103i \(-0.400048\pi\)
0.308875 + 0.951103i \(0.400048\pi\)
\(338\) −60.1680 −3.27271
\(339\) 30.7065 1.66775
\(340\) 29.5893 1.60470
\(341\) −22.6469 −1.22640
\(342\) −4.98834 −0.269738
\(343\) −9.57823 −0.517176
\(344\) −37.6705 −2.03106
\(345\) 4.29298 0.231126
\(346\) 52.2325 2.80804
\(347\) −4.25810 −0.228587 −0.114293 0.993447i \(-0.536460\pi\)
−0.114293 + 0.993447i \(0.536460\pi\)
\(348\) 73.1845 3.92310
\(349\) −14.2385 −0.762169 −0.381085 0.924540i \(-0.624449\pi\)
−0.381085 + 0.924540i \(0.624449\pi\)
\(350\) 14.4659 0.773235
\(351\) 22.2524 1.18775
\(352\) −0.550157 −0.0293234
\(353\) 32.1199 1.70957 0.854785 0.518982i \(-0.173689\pi\)
0.854785 + 0.518982i \(0.173689\pi\)
\(354\) −27.7403 −1.47438
\(355\) 11.3313 0.601402
\(356\) −32.1186 −1.70228
\(357\) −28.0783 −1.48606
\(358\) 53.7020 2.83824
\(359\) −9.57670 −0.505439 −0.252719 0.967540i \(-0.581325\pi\)
−0.252719 + 0.967540i \(0.581325\pi\)
\(360\) 11.0222 0.580923
\(361\) −16.2892 −0.857326
\(362\) 2.51628 0.132253
\(363\) −10.8276 −0.568303
\(364\) −82.2074 −4.30884
\(365\) 14.1815 0.742295
\(366\) −15.8297 −0.827432
\(367\) 2.18672 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(368\) −4.80349 −0.250399
\(369\) 8.45483 0.440141
\(370\) −0.316243 −0.0164407
\(371\) 16.8452 0.874560
\(372\) −78.2707 −4.05814
\(373\) 13.1840 0.682640 0.341320 0.939947i \(-0.389126\pi\)
0.341320 + 0.939947i \(0.389126\pi\)
\(374\) 24.0464 1.24341
\(375\) 25.0380 1.29296
\(376\) −29.4611 −1.51934
\(377\) −54.1437 −2.78854
\(378\) 29.7447 1.52990
\(379\) −2.79393 −0.143515 −0.0717573 0.997422i \(-0.522861\pi\)
−0.0717573 + 0.997422i \(0.522861\pi\)
\(380\) −11.9107 −0.611008
\(381\) 28.0906 1.43913
\(382\) 47.8004 2.44568
\(383\) −15.3207 −0.782853 −0.391426 0.920209i \(-0.628018\pi\)
−0.391426 + 0.920209i \(0.628018\pi\)
\(384\) 39.9160 2.03696
\(385\) −14.3689 −0.732309
\(386\) −20.4456 −1.04065
\(387\) 9.36536 0.476068
\(388\) −69.3033 −3.51834
\(389\) 6.20522 0.314617 0.157309 0.987550i \(-0.449718\pi\)
0.157309 + 0.987550i \(0.449718\pi\)
\(390\) −55.6207 −2.81646
\(391\) 4.74560 0.239995
\(392\) −20.5018 −1.03550
\(393\) −28.1245 −1.41870
\(394\) −26.4592 −1.33299
\(395\) 21.8168 1.09772
\(396\) 11.8975 0.597874
\(397\) 15.3064 0.768206 0.384103 0.923290i \(-0.374511\pi\)
0.384103 + 0.923290i \(0.374511\pi\)
\(398\) 24.5823 1.23220
\(399\) 11.3025 0.565833
\(400\) −7.31502 −0.365751
\(401\) 18.6056 0.929120 0.464560 0.885542i \(-0.346212\pi\)
0.464560 + 0.885542i \(0.346212\pi\)
\(402\) −13.3599 −0.666332
\(403\) 57.9066 2.88453
\(404\) 25.4938 1.26836
\(405\) 20.1018 0.998865
\(406\) −72.3736 −3.59184
\(407\) −0.171665 −0.00850913
\(408\) 41.7940 2.06911
\(409\) 28.3336 1.40101 0.700503 0.713649i \(-0.252959\pi\)
0.700503 + 0.713649i \(0.252959\pi\)
\(410\) 30.2233 1.49262
\(411\) −20.5704 −1.01466
\(412\) −16.6676 −0.821156
\(413\) 18.3240 0.901663
\(414\) 3.51522 0.172764
\(415\) 19.8006 0.971972
\(416\) 1.40671 0.0689698
\(417\) −37.2761 −1.82542
\(418\) −9.67952 −0.473441
\(419\) −10.5239 −0.514128 −0.257064 0.966394i \(-0.582755\pi\)
−0.257064 + 0.966394i \(0.582755\pi\)
\(420\) −49.6610 −2.42321
\(421\) 1.50742 0.0734674 0.0367337 0.999325i \(-0.488305\pi\)
0.0367337 + 0.999325i \(0.488305\pi\)
\(422\) −4.23734 −0.206270
\(423\) 7.32440 0.356125
\(424\) −25.0738 −1.21769
\(425\) 7.22687 0.350555
\(426\) 31.8262 1.54198
\(427\) 10.4564 0.506019
\(428\) 30.1379 1.45677
\(429\) −30.1924 −1.45770
\(430\) 33.4781 1.61446
\(431\) 6.17775 0.297572 0.148786 0.988869i \(-0.452463\pi\)
0.148786 + 0.988869i \(0.452463\pi\)
\(432\) −15.0411 −0.723666
\(433\) −5.58124 −0.268217 −0.134109 0.990967i \(-0.542817\pi\)
−0.134109 + 0.990967i \(0.542817\pi\)
\(434\) 77.4034 3.71548
\(435\) −32.7079 −1.56822
\(436\) −19.7424 −0.945489
\(437\) −1.91027 −0.0913808
\(438\) 39.8317 1.90323
\(439\) 11.4853 0.548164 0.274082 0.961706i \(-0.411626\pi\)
0.274082 + 0.961706i \(0.411626\pi\)
\(440\) 21.3879 1.01963
\(441\) 5.09702 0.242715
\(442\) −61.4850 −2.92454
\(443\) 6.23410 0.296191 0.148096 0.988973i \(-0.452686\pi\)
0.148096 + 0.988973i \(0.452686\pi\)
\(444\) −0.593298 −0.0281567
\(445\) 14.3546 0.680472
\(446\) 27.6804 1.31071
\(447\) 10.8931 0.515224
\(448\) −25.7423 −1.21621
\(449\) −19.2240 −0.907236 −0.453618 0.891196i \(-0.649867\pi\)
−0.453618 + 0.891196i \(0.649867\pi\)
\(450\) 5.35318 0.252351
\(451\) 16.4060 0.772529
\(452\) 60.0354 2.82383
\(453\) −43.4043 −2.03931
\(454\) 42.0237 1.97227
\(455\) 36.7404 1.72242
\(456\) −16.8236 −0.787835
\(457\) −25.1834 −1.17803 −0.589016 0.808121i \(-0.700485\pi\)
−0.589016 + 0.808121i \(0.700485\pi\)
\(458\) 17.2304 0.805125
\(459\) 14.8598 0.693598
\(460\) 8.39336 0.391342
\(461\) −29.5473 −1.37616 −0.688078 0.725636i \(-0.741545\pi\)
−0.688078 + 0.725636i \(0.741545\pi\)
\(462\) −40.3580 −1.87763
\(463\) 24.9805 1.16094 0.580471 0.814281i \(-0.302868\pi\)
0.580471 + 0.814281i \(0.302868\pi\)
\(464\) 36.5974 1.69899
\(465\) 34.9810 1.62221
\(466\) −61.9366 −2.86916
\(467\) 18.8022 0.870061 0.435030 0.900416i \(-0.356738\pi\)
0.435030 + 0.900416i \(0.356738\pi\)
\(468\) −30.4212 −1.40622
\(469\) 8.82494 0.407498
\(470\) 26.1824 1.20770
\(471\) 11.5432 0.531882
\(472\) −27.2749 −1.25543
\(473\) 18.1728 0.835588
\(474\) 61.2767 2.81453
\(475\) −2.90907 −0.133477
\(476\) −54.8969 −2.51619
\(477\) 6.23366 0.285419
\(478\) −39.7146 −1.81651
\(479\) −2.90297 −0.132640 −0.0663201 0.997798i \(-0.521126\pi\)
−0.0663201 + 0.997798i \(0.521126\pi\)
\(480\) 0.849787 0.0387873
\(481\) 0.438937 0.0200138
\(482\) 50.2663 2.28957
\(483\) −7.96474 −0.362408
\(484\) −21.1695 −0.962250
\(485\) 30.9733 1.40643
\(486\) 29.7109 1.34771
\(487\) 13.1114 0.594132 0.297066 0.954857i \(-0.403992\pi\)
0.297066 + 0.954857i \(0.403992\pi\)
\(488\) −15.5641 −0.704553
\(489\) 30.0141 1.35728
\(490\) 18.2202 0.823104
\(491\) 23.7244 1.07067 0.535333 0.844641i \(-0.320186\pi\)
0.535333 + 0.844641i \(0.320186\pi\)
\(492\) 56.7014 2.55629
\(493\) −36.1564 −1.62840
\(494\) 24.7499 1.11355
\(495\) −5.31730 −0.238995
\(496\) −39.1409 −1.75748
\(497\) −21.0229 −0.943004
\(498\) 55.6139 2.49212
\(499\) 13.0002 0.581967 0.290983 0.956728i \(-0.406018\pi\)
0.290983 + 0.956728i \(0.406018\pi\)
\(500\) 48.9528 2.18924
\(501\) −45.4357 −2.02992
\(502\) 53.2844 2.37820
\(503\) 20.1820 0.899871 0.449936 0.893061i \(-0.351447\pi\)
0.449936 + 0.893061i \(0.351447\pi\)
\(504\) −20.4495 −0.910893
\(505\) −11.3938 −0.507016
\(506\) 6.82104 0.303232
\(507\) 50.4488 2.24051
\(508\) 54.9210 2.43672
\(509\) 22.0919 0.979205 0.489603 0.871946i \(-0.337142\pi\)
0.489603 + 0.871946i \(0.337142\pi\)
\(510\) −37.1427 −1.64471
\(511\) −26.3109 −1.16393
\(512\) 40.1649 1.77505
\(513\) −5.98161 −0.264095
\(514\) 74.9201 3.30458
\(515\) 7.44917 0.328249
\(516\) 62.8077 2.76496
\(517\) 14.2125 0.625065
\(518\) 0.586724 0.0257792
\(519\) −43.7951 −1.92239
\(520\) −54.6874 −2.39820
\(521\) 33.0366 1.44736 0.723680 0.690136i \(-0.242449\pi\)
0.723680 + 0.690136i \(0.242449\pi\)
\(522\) −26.7822 −1.17223
\(523\) 0.267661 0.0117040 0.00585200 0.999983i \(-0.498137\pi\)
0.00585200 + 0.999983i \(0.498137\pi\)
\(524\) −54.9873 −2.40213
\(525\) −12.1292 −0.529360
\(526\) −30.0432 −1.30995
\(527\) 38.6692 1.68446
\(528\) 20.4080 0.888144
\(529\) −21.6539 −0.941472
\(530\) 22.2833 0.967924
\(531\) 6.78087 0.294265
\(532\) 22.0979 0.958067
\(533\) −41.9491 −1.81702
\(534\) 40.3177 1.74472
\(535\) −13.4694 −0.582331
\(536\) −13.1357 −0.567378
\(537\) −45.0273 −1.94307
\(538\) 12.7189 0.548352
\(539\) 9.89041 0.426010
\(540\) 26.2820 1.13100
\(541\) −2.23202 −0.0959619 −0.0479809 0.998848i \(-0.515279\pi\)
−0.0479809 + 0.998848i \(0.515279\pi\)
\(542\) −18.1638 −0.780202
\(543\) −2.10982 −0.0905409
\(544\) 0.939383 0.0402757
\(545\) 8.82334 0.377950
\(546\) 103.193 4.41625
\(547\) −35.3960 −1.51342 −0.756711 0.653750i \(-0.773195\pi\)
−0.756711 + 0.653750i \(0.773195\pi\)
\(548\) −40.2179 −1.71802
\(549\) 3.86943 0.165143
\(550\) 10.3875 0.442923
\(551\) 14.5542 0.620031
\(552\) 11.8554 0.504597
\(553\) −40.4765 −1.72124
\(554\) −22.6440 −0.962051
\(555\) 0.265159 0.0112554
\(556\) −72.8799 −3.09080
\(557\) −11.4950 −0.487057 −0.243528 0.969894i \(-0.578305\pi\)
−0.243528 + 0.969894i \(0.578305\pi\)
\(558\) 28.6435 1.21258
\(559\) −46.4667 −1.96533
\(560\) −24.8340 −1.04943
\(561\) −20.1621 −0.851243
\(562\) 32.6097 1.37556
\(563\) −16.2612 −0.685328 −0.342664 0.939458i \(-0.611329\pi\)
−0.342664 + 0.939458i \(0.611329\pi\)
\(564\) 49.1203 2.06834
\(565\) −26.8312 −1.12880
\(566\) −53.6119 −2.25348
\(567\) −37.2947 −1.56623
\(568\) 31.2921 1.31299
\(569\) −20.8098 −0.872392 −0.436196 0.899852i \(-0.643675\pi\)
−0.436196 + 0.899852i \(0.643675\pi\)
\(570\) 14.9513 0.626239
\(571\) 34.6094 1.44836 0.724180 0.689612i \(-0.242219\pi\)
0.724180 + 0.689612i \(0.242219\pi\)
\(572\) −59.0303 −2.46818
\(573\) −40.0790 −1.67432
\(574\) −56.0731 −2.34045
\(575\) 2.04999 0.0854904
\(576\) −9.52606 −0.396919
\(577\) 38.2923 1.59413 0.797066 0.603893i \(-0.206384\pi\)
0.797066 + 0.603893i \(0.206384\pi\)
\(578\) 0.663184 0.0275848
\(579\) 17.1429 0.712436
\(580\) −63.9484 −2.65531
\(581\) −36.7359 −1.52406
\(582\) 86.9947 3.60605
\(583\) 12.0960 0.500964
\(584\) 39.1633 1.62059
\(585\) 13.5960 0.562124
\(586\) −31.0326 −1.28194
\(587\) −21.9669 −0.906671 −0.453335 0.891340i \(-0.649766\pi\)
−0.453335 + 0.891340i \(0.649766\pi\)
\(588\) 34.1826 1.40967
\(589\) −15.5657 −0.641374
\(590\) 24.2394 0.997921
\(591\) 22.1851 0.912574
\(592\) −0.296691 −0.0121939
\(593\) −37.3898 −1.53541 −0.767707 0.640802i \(-0.778602\pi\)
−0.767707 + 0.640802i \(0.778602\pi\)
\(594\) 21.3586 0.876356
\(595\) 24.5347 1.00583
\(596\) 21.2974 0.872376
\(597\) −20.6114 −0.843569
\(598\) −17.4410 −0.713214
\(599\) −14.3567 −0.586599 −0.293299 0.956021i \(-0.594753\pi\)
−0.293299 + 0.956021i \(0.594753\pi\)
\(600\) 18.0540 0.737052
\(601\) −45.1903 −1.84335 −0.921675 0.387962i \(-0.873179\pi\)
−0.921675 + 0.387962i \(0.873179\pi\)
\(602\) −62.1118 −2.53149
\(603\) 3.26571 0.132990
\(604\) −84.8613 −3.45296
\(605\) 9.46115 0.384650
\(606\) −32.0017 −1.29998
\(607\) 22.8345 0.926823 0.463412 0.886143i \(-0.346625\pi\)
0.463412 + 0.886143i \(0.346625\pi\)
\(608\) −0.378135 −0.0153354
\(609\) 60.6828 2.45899
\(610\) 13.8320 0.560039
\(611\) −36.3404 −1.47018
\(612\) −20.3149 −0.821180
\(613\) 14.4611 0.584079 0.292040 0.956406i \(-0.405666\pi\)
0.292040 + 0.956406i \(0.405666\pi\)
\(614\) 39.5694 1.59689
\(615\) −25.3412 −1.02186
\(616\) −39.6808 −1.59879
\(617\) −21.3647 −0.860109 −0.430055 0.902803i \(-0.641506\pi\)
−0.430055 + 0.902803i \(0.641506\pi\)
\(618\) 20.9225 0.841625
\(619\) −10.4054 −0.418230 −0.209115 0.977891i \(-0.567058\pi\)
−0.209115 + 0.977891i \(0.567058\pi\)
\(620\) 68.3926 2.74671
\(621\) 4.21517 0.169149
\(622\) 24.6619 0.988852
\(623\) −26.6320 −1.06699
\(624\) −52.1819 −2.08895
\(625\) −13.0438 −0.521752
\(626\) 66.2893 2.64945
\(627\) 8.11594 0.324120
\(628\) 22.5685 0.900582
\(629\) 0.293116 0.0116873
\(630\) 18.1737 0.724056
\(631\) 22.0522 0.877885 0.438942 0.898515i \(-0.355353\pi\)
0.438942 + 0.898515i \(0.355353\pi\)
\(632\) 60.2485 2.39656
\(633\) 3.55286 0.141214
\(634\) 10.9814 0.436129
\(635\) −24.5455 −0.974058
\(636\) 41.8053 1.65769
\(637\) −25.2891 −1.00199
\(638\) −51.9690 −2.05747
\(639\) −7.77961 −0.307757
\(640\) −34.8785 −1.37869
\(641\) 16.5002 0.651718 0.325859 0.945418i \(-0.394347\pi\)
0.325859 + 0.945418i \(0.394347\pi\)
\(642\) −37.8314 −1.49309
\(643\) 2.83706 0.111883 0.0559414 0.998434i \(-0.482184\pi\)
0.0559414 + 0.998434i \(0.482184\pi\)
\(644\) −15.5722 −0.613629
\(645\) −28.0703 −1.10527
\(646\) 16.5276 0.650270
\(647\) −9.84659 −0.387109 −0.193555 0.981089i \(-0.562002\pi\)
−0.193555 + 0.981089i \(0.562002\pi\)
\(648\) 55.5124 2.18073
\(649\) 13.1578 0.516489
\(650\) −26.5601 −1.04177
\(651\) −64.9001 −2.54364
\(652\) 58.6816 2.29815
\(653\) −46.5592 −1.82200 −0.911002 0.412402i \(-0.864690\pi\)
−0.911002 + 0.412402i \(0.864690\pi\)
\(654\) 24.7821 0.969058
\(655\) 24.5751 0.960230
\(656\) 28.3547 1.10707
\(657\) −9.73649 −0.379857
\(658\) −48.5760 −1.89369
\(659\) −10.5390 −0.410539 −0.205270 0.978705i \(-0.565807\pi\)
−0.205270 + 0.978705i \(0.565807\pi\)
\(660\) −35.6598 −1.38806
\(661\) −21.1487 −0.822589 −0.411294 0.911503i \(-0.634923\pi\)
−0.411294 + 0.911503i \(0.634923\pi\)
\(662\) −17.9004 −0.695720
\(663\) 51.5530 2.00215
\(664\) 54.6807 2.12202
\(665\) −9.87609 −0.382978
\(666\) 0.217120 0.00841324
\(667\) −10.2562 −0.397121
\(668\) −88.8330 −3.43705
\(669\) −23.2091 −0.897315
\(670\) 11.6739 0.451001
\(671\) 7.50836 0.289857
\(672\) −1.57661 −0.0608189
\(673\) −46.8511 −1.80598 −0.902989 0.429664i \(-0.858632\pi\)
−0.902989 + 0.429664i \(0.858632\pi\)
\(674\) −27.8319 −1.07205
\(675\) 6.41910 0.247071
\(676\) 98.6342 3.79362
\(677\) −0.579010 −0.0222532 −0.0111266 0.999938i \(-0.503542\pi\)
−0.0111266 + 0.999938i \(0.503542\pi\)
\(678\) −75.3609 −2.89422
\(679\) −57.4646 −2.20529
\(680\) −36.5194 −1.40046
\(681\) −35.2354 −1.35022
\(682\) 55.5808 2.12830
\(683\) 41.3272 1.58134 0.790671 0.612241i \(-0.209732\pi\)
0.790671 + 0.612241i \(0.209732\pi\)
\(684\) 8.17745 0.312673
\(685\) 17.9743 0.686763
\(686\) 23.5072 0.897510
\(687\) −14.4471 −0.551192
\(688\) 31.4083 1.19743
\(689\) −30.9286 −1.17829
\(690\) −10.5360 −0.401097
\(691\) 35.2881 1.34242 0.671210 0.741267i \(-0.265775\pi\)
0.671210 + 0.741267i \(0.265775\pi\)
\(692\) −85.6254 −3.25499
\(693\) 9.86516 0.374746
\(694\) 10.4504 0.396691
\(695\) 32.5718 1.23552
\(696\) −90.3251 −3.42376
\(697\) −28.0130 −1.06107
\(698\) 34.9446 1.32267
\(699\) 51.9317 1.96424
\(700\) −23.7142 −0.896311
\(701\) −11.9185 −0.450157 −0.225079 0.974341i \(-0.572264\pi\)
−0.225079 + 0.974341i \(0.572264\pi\)
\(702\) −54.6126 −2.06122
\(703\) −0.117989 −0.00445005
\(704\) −18.4847 −0.696667
\(705\) −21.9530 −0.826798
\(706\) −78.8297 −2.96680
\(707\) 21.1388 0.795006
\(708\) 45.4751 1.70906
\(709\) −24.6289 −0.924959 −0.462480 0.886630i \(-0.653040\pi\)
−0.462480 + 0.886630i \(0.653040\pi\)
\(710\) −27.8096 −1.04368
\(711\) −14.9785 −0.561739
\(712\) 39.6412 1.48562
\(713\) 10.9690 0.410791
\(714\) 68.9107 2.57892
\(715\) 26.3820 0.986632
\(716\) −88.0345 −3.29000
\(717\) 33.2994 1.24359
\(718\) 23.5035 0.877141
\(719\) 28.1922 1.05139 0.525695 0.850673i \(-0.323805\pi\)
0.525695 + 0.850673i \(0.323805\pi\)
\(720\) −9.18994 −0.342489
\(721\) −13.8204 −0.514699
\(722\) 39.9775 1.48781
\(723\) −42.1466 −1.56745
\(724\) −4.12498 −0.153304
\(725\) −15.6187 −0.580064
\(726\) 26.5735 0.986236
\(727\) −36.5849 −1.35686 −0.678429 0.734666i \(-0.737339\pi\)
−0.678429 + 0.734666i \(0.737339\pi\)
\(728\) 101.461 3.76040
\(729\) 8.62695 0.319517
\(730\) −34.8048 −1.28818
\(731\) −31.0298 −1.14768
\(732\) 25.9499 0.959135
\(733\) −39.2120 −1.44833 −0.724164 0.689628i \(-0.757774\pi\)
−0.724164 + 0.689628i \(0.757774\pi\)
\(734\) −5.36673 −0.198090
\(735\) −15.2770 −0.563501
\(736\) 0.266467 0.00982211
\(737\) 6.33689 0.233422
\(738\) −20.7501 −0.763823
\(739\) 46.6007 1.71424 0.857118 0.515121i \(-0.172253\pi\)
0.857118 + 0.515121i \(0.172253\pi\)
\(740\) 0.518422 0.0190576
\(741\) −20.7519 −0.762341
\(742\) −41.3421 −1.51772
\(743\) −18.6904 −0.685683 −0.342841 0.939393i \(-0.611389\pi\)
−0.342841 + 0.939393i \(0.611389\pi\)
\(744\) 96.6025 3.54162
\(745\) −9.51832 −0.348724
\(746\) −32.3565 −1.18466
\(747\) −13.5943 −0.497390
\(748\) −39.4196 −1.44132
\(749\) 24.9896 0.913102
\(750\) −61.4492 −2.24381
\(751\) 33.6658 1.22848 0.614241 0.789118i \(-0.289462\pi\)
0.614241 + 0.789118i \(0.289462\pi\)
\(752\) 24.5636 0.895743
\(753\) −44.6771 −1.62812
\(754\) 132.881 4.83925
\(755\) 37.9265 1.38029
\(756\) −48.7609 −1.77342
\(757\) 16.0511 0.583389 0.291694 0.956512i \(-0.405781\pi\)
0.291694 + 0.956512i \(0.405781\pi\)
\(758\) 6.85696 0.249056
\(759\) −5.71921 −0.207594
\(760\) 14.7004 0.533238
\(761\) 7.56687 0.274299 0.137149 0.990550i \(-0.456206\pi\)
0.137149 + 0.990550i \(0.456206\pi\)
\(762\) −68.9409 −2.49747
\(763\) −16.3699 −0.592630
\(764\) −78.3599 −2.83496
\(765\) 9.07919 0.328259
\(766\) 37.6006 1.35857
\(767\) −33.6437 −1.21480
\(768\) −66.2052 −2.38897
\(769\) −4.77046 −0.172027 −0.0860135 0.996294i \(-0.527413\pi\)
−0.0860135 + 0.996294i \(0.527413\pi\)
\(770\) 35.2647 1.27085
\(771\) −62.8179 −2.26233
\(772\) 33.5168 1.20629
\(773\) 51.2454 1.84317 0.921585 0.388177i \(-0.126895\pi\)
0.921585 + 0.388177i \(0.126895\pi\)
\(774\) −22.9848 −0.826171
\(775\) 16.7042 0.600032
\(776\) 85.5349 3.07052
\(777\) −0.491948 −0.0176485
\(778\) −15.2290 −0.545988
\(779\) 11.2762 0.404013
\(780\) 91.1798 3.26476
\(781\) −15.0958 −0.540170
\(782\) −11.6468 −0.416489
\(783\) −32.1151 −1.14770
\(784\) 17.0937 0.610490
\(785\) −10.0864 −0.359999
\(786\) 69.0242 2.46201
\(787\) −17.9526 −0.639942 −0.319971 0.947427i \(-0.603673\pi\)
−0.319971 + 0.947427i \(0.603673\pi\)
\(788\) 43.3749 1.54517
\(789\) 25.1902 0.896794
\(790\) −53.5434 −1.90499
\(791\) 49.7799 1.76997
\(792\) −14.6841 −0.521776
\(793\) −19.1984 −0.681754
\(794\) −37.5654 −1.33315
\(795\) −18.6838 −0.662645
\(796\) −40.2981 −1.42833
\(797\) 6.23298 0.220783 0.110392 0.993888i \(-0.464789\pi\)
0.110392 + 0.993888i \(0.464789\pi\)
\(798\) −27.7390 −0.981949
\(799\) −24.2676 −0.858526
\(800\) 0.405791 0.0143469
\(801\) −9.85529 −0.348220
\(802\) −45.6625 −1.61240
\(803\) −18.8930 −0.666719
\(804\) 21.9011 0.772393
\(805\) 6.95957 0.245292
\(806\) −142.116 −5.00583
\(807\) −10.6644 −0.375404
\(808\) −31.4647 −1.10692
\(809\) −21.5073 −0.756156 −0.378078 0.925774i \(-0.623415\pi\)
−0.378078 + 0.925774i \(0.623415\pi\)
\(810\) −49.3344 −1.73343
\(811\) −35.2682 −1.23843 −0.619216 0.785220i \(-0.712550\pi\)
−0.619216 + 0.785220i \(0.712550\pi\)
\(812\) 118.643 4.16356
\(813\) 15.2297 0.534129
\(814\) 0.421307 0.0147668
\(815\) −26.2262 −0.918664
\(816\) −34.8463 −1.21987
\(817\) 12.4906 0.436991
\(818\) −69.5373 −2.43131
\(819\) −25.2245 −0.881417
\(820\) −49.5455 −1.73020
\(821\) 32.2222 1.12456 0.562282 0.826946i \(-0.309924\pi\)
0.562282 + 0.826946i \(0.309924\pi\)
\(822\) 50.4845 1.76085
\(823\) 37.9085 1.32141 0.660704 0.750647i \(-0.270258\pi\)
0.660704 + 0.750647i \(0.270258\pi\)
\(824\) 20.5714 0.716638
\(825\) −8.70953 −0.303227
\(826\) −44.9713 −1.56475
\(827\) 14.4159 0.501290 0.250645 0.968079i \(-0.419357\pi\)
0.250645 + 0.968079i \(0.419357\pi\)
\(828\) −5.76255 −0.200263
\(829\) 9.87242 0.342883 0.171442 0.985194i \(-0.445157\pi\)
0.171442 + 0.985194i \(0.445157\pi\)
\(830\) −48.5952 −1.68677
\(831\) 18.9862 0.658624
\(832\) 47.2641 1.63859
\(833\) −16.8877 −0.585124
\(834\) 91.4843 3.16784
\(835\) 39.7016 1.37393
\(836\) 15.8678 0.548799
\(837\) 34.3470 1.18721
\(838\) 25.8282 0.892220
\(839\) −1.78012 −0.0614566 −0.0307283 0.999528i \(-0.509783\pi\)
−0.0307283 + 0.999528i \(0.509783\pi\)
\(840\) 61.2921 2.11478
\(841\) 49.1412 1.69452
\(842\) −3.69957 −0.127496
\(843\) −27.3421 −0.941712
\(844\) 6.94633 0.239103
\(845\) −44.0820 −1.51647
\(846\) −17.9758 −0.618021
\(847\) −17.5532 −0.603136
\(848\) 20.9056 0.717902
\(849\) 44.9517 1.54274
\(850\) −17.7364 −0.608354
\(851\) 0.0831457 0.00285020
\(852\) −52.1731 −1.78742
\(853\) −30.6223 −1.04849 −0.524244 0.851568i \(-0.675652\pi\)
−0.524244 + 0.851568i \(0.675652\pi\)
\(854\) −25.6624 −0.878148
\(855\) −3.65470 −0.124988
\(856\) −37.1966 −1.27135
\(857\) −7.51221 −0.256612 −0.128306 0.991735i \(-0.540954\pi\)
−0.128306 + 0.991735i \(0.540954\pi\)
\(858\) 74.0992 2.52971
\(859\) −26.1130 −0.890965 −0.445482 0.895291i \(-0.646968\pi\)
−0.445482 + 0.895291i \(0.646968\pi\)
\(860\) −54.8812 −1.87143
\(861\) 47.0154 1.60228
\(862\) −15.1616 −0.516408
\(863\) −28.2339 −0.961091 −0.480546 0.876970i \(-0.659561\pi\)
−0.480546 + 0.876970i \(0.659561\pi\)
\(864\) 0.834385 0.0283864
\(865\) 38.2680 1.30115
\(866\) 13.6977 0.465465
\(867\) −0.556057 −0.0188847
\(868\) −126.889 −4.30688
\(869\) −29.0648 −0.985956
\(870\) 80.2728 2.72150
\(871\) −16.2030 −0.549018
\(872\) 24.3663 0.825146
\(873\) −21.2651 −0.719713
\(874\) 4.68826 0.158583
\(875\) 40.5905 1.37221
\(876\) −65.2966 −2.20617
\(877\) −13.4117 −0.452879 −0.226440 0.974025i \(-0.572709\pi\)
−0.226440 + 0.974025i \(0.572709\pi\)
\(878\) −28.1876 −0.951287
\(879\) 26.0197 0.877624
\(880\) −17.8324 −0.601132
\(881\) 13.3596 0.450095 0.225048 0.974348i \(-0.427746\pi\)
0.225048 + 0.974348i \(0.427746\pi\)
\(882\) −12.5093 −0.421209
\(883\) −29.8463 −1.00441 −0.502204 0.864749i \(-0.667477\pi\)
−0.502204 + 0.864749i \(0.667477\pi\)
\(884\) 100.793 3.39004
\(885\) −20.3239 −0.683181
\(886\) −15.2999 −0.514011
\(887\) 52.8372 1.77410 0.887049 0.461675i \(-0.152751\pi\)
0.887049 + 0.461675i \(0.152751\pi\)
\(888\) 0.732255 0.0245729
\(889\) 45.5391 1.52733
\(890\) −35.2295 −1.18089
\(891\) −26.7801 −0.897166
\(892\) −45.3769 −1.51933
\(893\) 9.76857 0.326893
\(894\) −26.7341 −0.894122
\(895\) 39.3447 1.31515
\(896\) 64.7099 2.16181
\(897\) 14.6236 0.488269
\(898\) 47.1801 1.57442
\(899\) −83.5718 −2.78728
\(900\) −8.77554 −0.292518
\(901\) −20.6537 −0.688073
\(902\) −40.2642 −1.34065
\(903\) 52.0786 1.73307
\(904\) −74.0963 −2.46441
\(905\) 1.84355 0.0612817
\(906\) 106.524 3.53903
\(907\) 10.2924 0.341755 0.170877 0.985292i \(-0.445340\pi\)
0.170877 + 0.985292i \(0.445340\pi\)
\(908\) −68.8901 −2.28620
\(909\) 7.82252 0.259456
\(910\) −90.1696 −2.98909
\(911\) −8.10401 −0.268498 −0.134249 0.990948i \(-0.542862\pi\)
−0.134249 + 0.990948i \(0.542862\pi\)
\(912\) 14.0269 0.464476
\(913\) −26.3788 −0.873011
\(914\) 61.8060 2.04436
\(915\) −11.5976 −0.383405
\(916\) −28.2461 −0.933277
\(917\) −45.5941 −1.50565
\(918\) −36.4695 −1.20367
\(919\) −53.3408 −1.75955 −0.879776 0.475388i \(-0.842308\pi\)
−0.879776 + 0.475388i \(0.842308\pi\)
\(920\) −10.3592 −0.341532
\(921\) −33.1776 −1.09324
\(922\) 72.5161 2.38819
\(923\) 38.5990 1.27050
\(924\) 66.1595 2.17649
\(925\) 0.126619 0.00416321
\(926\) −61.3080 −2.01471
\(927\) −5.11431 −0.167976
\(928\) −2.03019 −0.0666444
\(929\) −53.9902 −1.77136 −0.885680 0.464296i \(-0.846308\pi\)
−0.885680 + 0.464296i \(0.846308\pi\)
\(930\) −85.8515 −2.81518
\(931\) 6.79790 0.222792
\(932\) 101.534 3.32584
\(933\) −20.6781 −0.676972
\(934\) −46.1449 −1.50991
\(935\) 17.6175 0.576155
\(936\) 37.5462 1.22724
\(937\) 22.6819 0.740984 0.370492 0.928836i \(-0.379189\pi\)
0.370492 + 0.928836i \(0.379189\pi\)
\(938\) −21.6585 −0.707174
\(939\) −55.5813 −1.81383
\(940\) −42.9211 −1.39993
\(941\) 41.9097 1.36622 0.683108 0.730318i \(-0.260628\pi\)
0.683108 + 0.730318i \(0.260628\pi\)
\(942\) −28.3297 −0.923031
\(943\) −7.94622 −0.258765
\(944\) 22.7408 0.740150
\(945\) 21.7924 0.708907
\(946\) −44.6004 −1.45008
\(947\) 29.6824 0.964548 0.482274 0.876020i \(-0.339811\pi\)
0.482274 + 0.876020i \(0.339811\pi\)
\(948\) −100.452 −3.26252
\(949\) 48.3081 1.56815
\(950\) 7.13954 0.231637
\(951\) −9.20756 −0.298576
\(952\) 67.7543 2.19593
\(953\) −45.4176 −1.47122 −0.735610 0.677405i \(-0.763104\pi\)
−0.735610 + 0.677405i \(0.763104\pi\)
\(954\) −15.2988 −0.495318
\(955\) 35.0209 1.13325
\(956\) 65.1048 2.10564
\(957\) 43.5742 1.40856
\(958\) 7.12457 0.230184
\(959\) −33.3477 −1.07685
\(960\) 28.5519 0.921509
\(961\) 58.3799 1.88322
\(962\) −1.07725 −0.0347320
\(963\) 9.24754 0.297998
\(964\) −82.4023 −2.65400
\(965\) −14.9794 −0.482205
\(966\) 19.5473 0.628925
\(967\) 51.5719 1.65844 0.829220 0.558923i \(-0.188785\pi\)
0.829220 + 0.558923i \(0.188785\pi\)
\(968\) 26.1276 0.839773
\(969\) −13.8578 −0.445178
\(970\) −76.0157 −2.44072
\(971\) −55.9459 −1.79539 −0.897695 0.440618i \(-0.854759\pi\)
−0.897695 + 0.440618i \(0.854759\pi\)
\(972\) −48.7055 −1.56223
\(973\) −60.4302 −1.93730
\(974\) −32.1783 −1.03106
\(975\) 22.2697 0.713201
\(976\) 12.9768 0.415377
\(977\) 59.7613 1.91193 0.955966 0.293477i \(-0.0948126\pi\)
0.955966 + 0.293477i \(0.0948126\pi\)
\(978\) −73.6615 −2.35544
\(979\) −19.1235 −0.611190
\(980\) −29.8686 −0.954118
\(981\) −6.05776 −0.193410
\(982\) −58.2252 −1.85804
\(983\) −2.19978 −0.0701621 −0.0350811 0.999384i \(-0.511169\pi\)
−0.0350811 + 0.999384i \(0.511169\pi\)
\(984\) −69.9814 −2.23093
\(985\) −19.3853 −0.617666
\(986\) 88.7362 2.82594
\(987\) 40.7293 1.29643
\(988\) −40.5729 −1.29079
\(989\) −8.80198 −0.279887
\(990\) 13.0499 0.414753
\(991\) −37.7818 −1.20018 −0.600089 0.799933i \(-0.704868\pi\)
−0.600089 + 0.799933i \(0.704868\pi\)
\(992\) 2.17129 0.0689385
\(993\) 15.0089 0.476293
\(994\) 51.5950 1.63649
\(995\) 18.0102 0.570962
\(996\) −91.1687 −2.88879
\(997\) −25.9810 −0.822826 −0.411413 0.911449i \(-0.634965\pi\)
−0.411413 + 0.911449i \(0.634965\pi\)
\(998\) −31.9054 −1.00995
\(999\) 0.260353 0.00823721
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6029.2.a.a.1.18 234
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6029.2.a.a.1.18 234 1.1 even 1 trivial